题目：Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows
报告人：黄俊涛 博士 清华大学
时间：9月6日 下午3:30-4:30
地点：学院二楼209
摘要：In this talk, we will present a family of second-order and third-order modified Patankar Runge-Kutta (MPRK) methods, which are conservative and unconditionally positivity-preserving, for production-destruction equations. We derive necessary and sufficient conditions to obtain the designed order of accuracy. This ordinary differential equation solver is then extended to solve a class of semi-discrete schemes for PDEs. Combining this time integration method with the positivity-preserving finite difference weighted essentially non-oscillatory (WENO) schemes, we successfully obtain a positivity-preserving WENO scheme for non-equilibrium flows. Various numerical tests are reported to demonstrate the effectiveness of the methods.
报告人简介:
Juntao Huang obtained his Ph.D. degree in mathematics in July 2018 at Tsinghua University and will continue his postdoctoral work in Michigan State Univerisity. During his Ph.D. study, he spent a year at Brown University as a visiting student from Sept 2015 to Sept 2016. His current research interest focuses on numerical solutions of partial differential equations. Topics of special interests include discontinuous Galerkin methods for hyperbolic equations and boundary treatments of some kinetic schemes.
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